Inovace bakalářského studijního oboru Aplikovaná chemie. Reg. č.: CZ.1.07/2.2.00/

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1 Inovace bakalářského studijního oboru Aplikovaná chemie Reg. č.: CZ.1.07/2.2.00/

2 Lecture vocabulary: State Equation Pressure Volume Temperature Quantity Unit Gas Value Mass Current Amount Substance Intensity Base, basic Derived Extensive Intensive Specific Composed of Set Random Move Interact Point Particle Obey Law State Amenable Increase, decrease Bubble Rise stav rovnice tlak objem teplota veličina jednotka plyn hodnota hmota, hmotnost proud (adj. současný) množství látka intenzita základní odvozený extenzivní intenzivní specifický (tj. vztažený na jednotku hmotnosti) složený z soubor náhodný pohybovat se interagovat bod částice řídit se zákon stav podléhající, přístupný zvýšení, snížení bublina stouat Surface (opposite = bulk)povrch (vnitřek) occupy proportional directly inversely rate container square root density molecular weight sum mixture individual component given liquid equilibrium zabírat, zaujímat, okupovat úměrný přímo nepřímo (též indirectly) rychlost nádoba odmocnina hustota molekulární hmotnost součet, suma směs jednotlivý složka daný, určitý kapalina rovnováha combine common formulation deviation finite behaviour interactions compressibility correction cohesion dew superheated liquid impossible vapor critical solve set of equations following expression obtain by application trick so-called reduced quantities dissappear common corresponding state kombinovat běžný formulace, tvar odchylka konečný chování interakce stlačitelnost oprava, korekce koheze, přilnavost, soudržnost rosa přehřátá kapalina nemožný pára kritický řešit soustava rovnic následující výraz získat aplikací, použitím trik, finta takzvané redukované veličiny zmizet společný, jednotný korespondující stav

3 Introduction to Physical Chemistry Lecture 1 Quantities, units and symbols in Physical Chemistry Ideal and real gas - gas laws Equation of state of the ideal gas Equations of state of real gases

4 Quantities, units and symbols in Physical Chemistry physical quantity = numerical value x unit Seven base quantities, others are derived quantities Extensive / intensive / specific / molar quantities

5 Ideal gas a theoretical gas composed of a set of randomly-moving, noninteracting point particles Properties: randomly-moving non-interacting point particles may be mono- di- atomic etc. Obeys: the ideal gas laws, a simplified equation of state, is amenable to analysis under statistical mechanics

6 Ideal gas laws Increase in size of bubbles as they rise to the surface

7 Other ideal gas laws Avogadro's law: the volume occupied by an ideal gas is proportional to the amount of moles (or molecules) present in the container. Graham's law: the rate at which gas molecules diffuse is inversely proportional to the square root of its density. Combined with Avogadro's law (i.e. since equal volumes have equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight. Dalton's law of partial pressures: the pressure of a mixture of gases simply is the sum of the partial pressures of the individual components. Henry's law: at a constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.

8 Ideal gas laws combine into the: Equation of state pv m 1834 Émile Clapeyron R( T ) celsius originally 267 For: a given amount of gas (1 mole), standard pressure ( kpa) and temperature (0 C) the volume of gas is: 22.42x10-3 m 3 3 p1v 1 p2v T T R 3 Pa m K mol or K J mol The common formulations are: pv nrt and p M RT

9 Real gas Deviations from ideal behaviour are caused by: finite volume of gas molecules interactions between molecules can be expressed by compressibility factor Van der Waal s equation 2 a n a p Vm b RT V ( ) p ( V nb) nrt 2 2 m V Correction for finite volume of molecules Correction for cohesion pressure

10 Van der Waals equation of state to the left of point F to the right of point G Light blue curves Red curve Dark blue curves Green sections normal liquid normal gas supercritical isotherms critical isotherm isotherms below the critical temperature metastable states Point F Point G Point K boiling point dew point critical point Line FG Section FA Section F A Section AC Section CG equilibrium of liquid and gaseous phases superheated liquid stretched liquid (p<0) analytic continuation of isotherm, physically impossible supercooled vapor

11 Critical parameters Van der Waals equation and critical parameters The critical point is an inflection on the critical isotherm. p k a Vm k b V ( ) 2, m, k RT k p V T 2 p 0, 2 V k T k 0 By solving the set of these three equations following expressions are obtained: p a V b T a k 8 2 ; m, k 3 ; k 27 b 27Rb

12 By application of an interesting mathematical trick, i.e. by substitution of the so-called reduced quantities defined as: pred p pk ; Vm, red Vm Vm, k ; Tred T Tk into vw equation, its reduced form is obtained: 3 pred 2 Vred 3Vred 1 8Tred Note that the parameters a and b disappeared, the equation is common for all gasses. This is the manifestation of the Theorem of corresponding states:

13 Equations of state of real gases Redlich Kwong model a RT pv ( m b) 1 ( V ) ( ) 2 m b V V bt m m The Virial equation derives from a perturbative treatment of statistical mechanics PV m BT C T DT RT Vm Vm Vm There are numerous other real gas state equations (Berthelot and modified Berthelot, Dieterici, Clausius, Peng Robinson, Wohl, Beattie Bridgeman, Benedict Webb Rubin)

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